A Hamiltonian formulation of the theory of induced gravity in two dimensions is constructed. This formulation differs from previous efforts in that the formalism is covariant under all relevant transformation groups. In particular, spatial diffeomorphism covariance and/or invariance is manifest throughout; the phase space carries a representation of the Lie algebra of the spacetime diffeomorphism group; the group of conformal isometries is projectively represented on the phase space as a symmetry group. The key ingredient that allows covariance with respect to the above groups is the enlargement of the gravitational phase space by the inclusion of the cotangent bundle over the space of embeddings of a Cauchy surface into the spacetime.